MATH 0015 Final Exam REVIEW REVISED: Fall 2020

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

For questions 1-9: Solve.1) -2z + 7 = -3z + 12 1)

A) 12 B) -12 C) -7 D) 5

2) 4(x + 5) - (3x + 4) = -4 2)A) x = - 20 B) x = 12 C) x = 5 D) x = 20

3) 25

x - 13

x = 3 3)

A) x = -90 B) x = 45 C) x = 90 D) x = -45

4) 15

(x + 6) = 16

(x + 8) 4)

A) x = -12 B) x = 3 C) x = -4 D) x = 4

5) -2(x - 3) - 59 = 3x - 5(x + 7) 5)A) -24 B) -94C) all real numbers D) no solution

6) 3(x + 7) = (3x + 21) 6)A) 0 B) 42C) all real numbers D) no solution

7) The length of a rectangular room is 4 feet longer than twice the width. If the room's perimeter is176 feet, what are the room's dimensions?

w

2w + 4

7)

A) Width = 56 ft; length = 120 ft B) Width = 28 ft; length = 60 ftC) Width = 42 ft; length = 46 ft D) Width = 33 ft; length = 70 ft

8) Four times the sum of some number and 3 is equal to 7 times the number minus 12. 8)A) 24 B) 8 C) -24 D) -8

9) A 12-ft. board is cut into 2 pieces so that one piece is 8 feet longer than 3 times the shorter piece. Ifthe shorter piece is x feet long, find the lengths of both pieces.

9)

A) shorter piece: 28 ft; longer piece: 36 ft B) shorter piece: 24 ft; longer piece: 44 ftC) shorter piece: 1 ft; longer piece: 11 ft D) shorter piece: 6 ft; longer piece: 36 ft

1

For questions 10-11: Solve the equation for the indicated variable.10) P = 2L + 2W for L 10)

A) L = d - 2W B) L = P - W C) L =P - W

2D) L =

P - 2W2

11) A = P + PRT for T 11)

A) T =PR

A - PB) T =

P - APR

C) T =AR

D) T =A - P

PR

For questions 12-13: Solve the inequality. Graph the solution set and write it in interval notation.12) 18x - 21 3(5x - 1) 12)

A) x < 6

B) x 6

C) x 6

D) x > 6

Solve the inequality. Graph the solution set and write it in interval notation.13) -8x + 8 -2(3x - 2) 13)

A) x 2

B) x 2

C) x < 2

D) x > 2

2

For questions 14-15: Describe the situation with a linear inequality and then solve the inequality.14) When making a long distance call from a certain pay phone, the first three minutes of a call cost

$1.10. After that, each additional minute or portion of a minute of that call costs $0.15. Use aninequality to find the number of minutes one can call long distance for $2.90.

14)

A) at most 12 minutes B) at most 15 minutesC) at most 3 minutes D) at most 19 minutes

15) A certain store has a fax machine available for use by its customers. The store charges $1.25 to sendthe first page and $0.40 for each subsequent page. Use an inequality to find the number of pagesthat can be faxed for $4.85

15)

A) at most 13 pages B) at most 10 pagesC) at most 4 pages D) at most 35 pages

Graph the equation.16) y = 3x - 6 16)

A) B)

C) D)

3

For questions 17-18: Graph the equation by plotting the intercepts.17) 4x - 8y = 24 17)

A) B)

C) D)

4

Graph the equation by plotting the intercepts.18) 5x - 15y = 30 18)

A) B)

C) D)

5

Graph the equation.19) -9y = -54 19)

A) B)

C) D)

6

Graph the line.

20) y = -34

x - 2 20)

A) B)

C) D)

For questions 21-23: Find the slope of a straight line that passes through the given pair of points.21) (-6, 11) and (7, 7) 21)

A) 18 B) - 134 C) -

413 D)

413

22) (8, 3) and (-8, 3) 22)A) 5 B) 2 C) 10 D) 0

23) (-6, -5) and (-3, 7) 23)A) 3 B) 12 C) 0 D) 4

7

Determine the rate of change. Don't forget to attach the proper units.24) The graph shows the total cost y (in dollars) of owning and operating a mini-van where x is the

number of miles driven.24)

A) $2.00 per mile B) cannot be determinedC) $21.00 per mile D) $0.50 per mile

For questions 25-26: Find the slope and the y-intercept.25) 2x - 3y = 6 25)

A) m =23 ; (0, -2) B) m = 2; (0, 6) C) m = -

23 ; (0, 2) D) m =

32 ; (0, 3)

26) x + 3y = 1 26)

A) m = -13 ; 0,

13 B) m =

13 ; 0,

13 C) m = -3; (0, 3) D) m = 1; (0, 1)

For questions 27-28: Write the equation of the line in slope-intercept form.27) m = -9, y-intercept (0, -2) 27)

A) y = 9x + 2 B) y = -2x - 9 C) y = 2x + 9 D) y = -9x - 2

28) m = 95

, y-intercept (0, -5) 28)

A) y = 95

x + 5 B) y = -95

x - 5 C) y = -95

x + 5 D) y = 95

x - 5

For questions 29-30: Find an equation of the line.29) vertical line through (5, -1) 29)

A) x = 5 B) x = -1 C) y = -1 D) y = 5

30) Horizontal line through (-8, 1) 30)A) x = 1 B) y = -8 C) x = -8 D) y = 1

Write an equation of the line passing through the given points.31) (5, -6) and (8, -12) 31)

A) y = - 12 x -

72 B) y = -2x + 4 C) y = 2x - 16 D) y =

12 x -

172

8

Write an equation of the line.32) 32)

A) x = -9 B) y = x - 9 C) y = -9 D) y = -9x

Find the domain and range of the relation.33) {(9, 9), (-10, -2), (-13, 3), (11, -3), (-1, 6)} 33)

A) Domain = {6, -2, 9, 3, -3}; range = {-1, -10, 9, -13, 11}B) Domain = {-1, 6, -10, -2, 9}; range = {9, -13, 3, 11, -3}C) Domain = {9, -13, 3, 11, -3}; range = {-1, 6, -10, -2, 9}D) Domain = {-1, -10, 9, -13, 11}; range = {6, -2, 9, 3, -3}

Determine whether the relation is a function.34) 34)

A) Not a function B) Function

Given the function, find the indicated value.35) f(x) = x2 + 4x + 6; f(-1) 35)

A) 11 B) -1 C) -9 D) 3

36) f(x) = 3 - 5x; f(-10) 36)A) -47 B) C) -50 D) -2

For numbers 37-42: Perform the indicated operation and simplify.37) (-7x9)(-4x7) 37)

A) -28x63 B) 28x63 C) 28x16 D) -28x16

9

38) -9x(2x + 8) 38)A) -18x2 - 72x B) -90x2 C) 2x2 - 72x D) -18x2 + 8x

39) 5x5(8x3 - 2x2 - 9) 39)A) 40x8 - 10x7 - 45x5 B) 40x3 - 10x2 - 45C) 40x8 - 2x2 - 9 D) 40x8 - 10x7

40) -9x2(10x5 + 3x3) 40)A) -117x7 - 117x5 B) -90x7 - 27x5 C) -117x2 D) -90x7 + 3x3

41) (5x + 6)2 41)A) 25x2 + 60x + 36 B) 5x2 + 60x + 36 C) 5x2 + 36 D) 25x2 + 36

42) (x - 6)(5x + 9) 42)A) 5x2 - 21x - 54 B) 5x2 - 21x - 21 C) 5x2 - 23x - 54 D) 5x2 - 54x - 21

Solve.43) Find the area of the top of the table. Express the area as a product, then multiply and simplify.

(12x + 5) inches(12x - 5) inches

43)

A) (144x2 - 25) sq in. B) (144x2 - 120x - 25) sq in.C) (x2 - 25) sq in. D) (144x2 + 120x - 25) sq in.

Simplify.

44) xy3

z5

544)

A) xy8

z10B) x5y15

z25C) xy15

z25D) x5y8

z10

45) 3x2y3

z3

445)

A) 81x8y12

z12B) 3x8y12

z7C) 81x6y7

z7D) 3x8y12

z12

10

46) (6a6b5c0)2 46)A) 36a12b10c2 B) 6a12b10 C) 36a12b10 D) 0

Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.

47) 21m12n11

3m11n747)

A) 7n4 B) 21mn4 C) 7mn4 D) 7m23n18

Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.

48) xy3

x3y

-248)

A) 1x5y7

B) 1x8y8

C) y4

x4D) x4

y4

49) (x-4y5)-3 49)

A) x12

y15B) y2

x-7C) x-7

y2D) 1

x12y15

50) 5x-3y-3

2z-250)

A) 4z2

125x3y3B) 2z2

5x3y3C) 5z2

2x3y3D) 5

2x3y3z2

Divide.

51) 36x9 - 8x6 + 40x3

4x351)

A) 9x6 - 2x3 + 10 B) 36x6 - 8x3 + 40C) 9x9 - 2x6 + 10x3 D) 9x6 + 2x3 - 10

Perform the division.

52) -21x6 + 21x5 - 12x4

-3x552)

A) 7x + 21x5 +4x

B) 7x - 7 +4x

C) 7x - 7 D) 11x - 7

For numbers 53 and 54: Factor the polynomial by factoring out a negative greatest common factor.53) -21y3 + 15y 53)

A) -3(7y3 + 5y) B) -3y(7y2 + 5) C) -3y(7y2 - 5) D) -3y2(7y - 5)

54) -10x4 + 15x3 - 5x2 54)A) -5x2(2x2 - 3x - 1) B) -5x2(2x2 + 3x - 1)C) -5x2(2x2 + 3x + 1) D) -5x2(2x2 - 3x + 1)

11

For numbers 55-60 : Factor the polynomial COMPLETELY. Write prime if the polynomial cannot be factored.55) 27x2 - 117x - 90 55)

A) 9(3x - 2)(x + 5) B) (27x + 18)(x - 5) C) prime D) 9(3x + 2)(x - 5)

56) xy2 + 3y2 - 25x - 75 56)A) (x + 3)(y - 5)2 B) (x - 3)(y + 5)(y - 5)C) (x + 3)(y + 5)(y - 5) D) (x + 3)(y2 - 25)

57) 10x2 + 6x - 15x - 9 57)A) (10x - 3)(x + 3) B) (2x + 3)(5x - 3) C) (10x + 3)(x - 3) D) (2x - 3)(5x + 3)

58) 15x2 + 20x - 12x - 16 58)A) (15x - 4)(x + 4) B) (5x - 4)(3x + 4) C) (5x + 4)(3x - 4) D) (15x + 4)(x - 4)

59) 6y2 - 13y + 6 59)A) (2y - 3)(3y - 2) B) (6y + 3)(y + 2) C) (2y + 3)(3y + 2) D) prime

60) 9x2 - 39x - 30 60)A) 3(3x + 2)(x - 5) B) 3(3x - 2)(x + 5) C) prime D) (9x + 6)(x - 5)

For questions 61-66: Solve the equation.61) x2 -4x = 0 61)

A) x = 0, x = -4 B) x = 0, x = 4 C) x = -4 D) x = 4

62) x2 - x = 56 62)A) x = -7, 8 B) x = 1, 56 C) x = 7, 8 D) x = -7, -8

63) 11d2 - 4d = 0 63)

A) d = -114

, 0 B) d = 114

, 0 C) d = 411

, 0 D) d = -411

, 0

Solve the problem.64) A window washer accidentally drops a bucket from the top of a 144-foot building. The height h of

the bucket after t seconds is given by h = -16t2 + 144. When will the bucket hit the ground?64)

A) -3 sec B) 9 sec C) 48 sec D) 3 sec

For numbers 65-66: Find any numbers for which the rational expression is undefined.

65) z - 27 - z

65)

A) z = -7 B) z = 7 C) z = 7, z = 2 D) none

66) 7y - 8y2 - 9

66)

A) y = 3 B) y = 3, y = -3 C) y =87 D) y = 9

12

Find the domain of the rational expression.

67) f(x) = 8x5 + x

67)

A) All real numbers except -5 B) All real number except 5C) All real numbers greate than 5 D) All real numbers except 0

For numbers 68-69: Solve the problem.68) The demand for a rooftop-mounted industrial air conditioner is given by the demand function

D(x) = 9800x2 + 5x

where x is the number of units produced each day and D(x) is the number sold each day. Assumethat x is an integer. What is the domain of the demand function from a purely mathematical pointof view?

68)

A) All integers greater than 0 B) All integers other than -5 or 0C) All integers D) All integers other than 5 or 0

Solve the problem.69) A drug is injected into a patient and the concentration of the drug is monitored. The drug's

concentration, C(t), in milligrams after t hours is modeled by C(t) = 4t3t2 + 4

. Estimate the drug's

concentration after 3 hours. (Round to the nearest hundredth.)

69)

A) 0.78 mg B) 0.39 mg C) 0.92 mg D) 0.25 mg

For problems 70-72: Perform the operation indicated and simplify.

70) (x - 10)25

÷5x - 50

2570)

A) 1x - 10

B) x - 10 C) 5(x - 10)25x - 50

D) (x - 10)325

71) x2 - 164y

÷4 - x28xy

71)

A) 7x(x + 4) B) -7x(x - 4) C) -7x(x + 4) D) 7x(x - 4)

72) x + 85 - x

÷x2 - 7x - 8

x2 - 13x + 4072)

A) x - 8x + 1

B) -(x + 8)(x - 8)

(x - 5)2C) -

x - 8x + 1

D) -x + 8x + 1

For problems 73-74: Simplify. Assume that all variables represent positive numbers.73) 75y2 73)

A) 5y 3 B) 5y2 3 C) 5 3y2 D) 5 3

74) 175x2y 74)A) 5xy2 7 B) 5xy 7 C) 5x2 7y D) 5x 7y

13

For problems 75-76: Solve the radical equation. Check all proposed solutions.75) 6x - 5 = 5 75)

A) x = 25 B) x = 103

C) x = 256

D) x = 5

76) 4x + 5 = 5 76)

A) x = 152

B) x = 25 C) x = 5 D) x = 254

Solve.77) A ball is thrown downward with an initial velocity of 14 meters per second from a cliff that is

80 meters high. The height of the ball is given by the quadratic equation h = -4.9t2 - 14t + 80 whereh is in meters and t is the time in seconds since the ball was thrown. Find the time it takes the ball tohit the ground. Round your answer to the nearest tenth of a second.

77)

A) 2.8 sec B) 3.9 sec C) 3.0 sec D) 2.9 sec

Sketch the graph of the quadratic function.78) f(x) = x2 - 2 78)

A) B)

C) D)

14

Answer KeyTestname: MATH0015 REVIEW AY20_21

1) D2) A3) B4) D5) D6) C7) B8) B9) C

10) D11) D12) B13) A14) B15) B16) C17) D18) A19) B20) B21) C22) D23) D24) D25) A26) A27) D28) D29) A30) D31) B32) C33) D34) A35) D36) B37) C38) A39) A40) B41) A42) A43) A44) B45) A46) C47) C48) D49) A50) C

15

Answer KeyTestname: MATH0015 REVIEW AY20_21

51) A52) B53) C54) D55) D56) C57) D58) B59) A60) A61) B62) A63) C64) D65) B66) B67) A68) B69) B70) B71) C72) D73) A74) D75) D76) C77) D78) B

16